Modulation of galactic cosmic rays in solar cycles 22–24: Analysis and physical interpretation

This work represents a physical interpretation of cosmic ray modulation in the 22nd–24th solar cycles, including an interpretation of an unusual behavior of their intensity in the last minimum of the solar activity (2008–2010). In terms of the Parker modulation model, which deals with regularly measured heliospheric characteristics, it is shown that the determining factor of the increased intensity of the galactic cosmic rays in the minimum of the 24th solar cycle is an anomalous reduction of the heliospheric magnetic field strength during this time interval under the additional influence of the solar wind velocity and the tilt angle of the heliospheric current sheet. We have used in the calculations the dependence of the diffusion tensor on the rigidity in the form K _ij ∝ R ^2?μ with μ = 1.2 in the sector zones of the heliospheric magnetic field and with μ = 0.8 outside the sector zones, which leads to an additional amplification of the diffusion mechanism of cosmic ray modulation. The proposed approach allows us to describe quite satisfactorily the integral intensity of protons with an energy above 0.1 GeV and the energy spectra in the minima of the 22nd–24th solar cycles at the same value of the free parameter. The determining factor of the anomalously high level of the galactic cosmic ray intensity in the minimum of the 24th solar cycle is the significant reduction of the heliospheric magnetic field strength during this time interval. The forecast of the intensity level in the minimum of the 25th solar cycle is provided.     

Climatic variables as indicators of solar activity

Tree-ring analysis is used successfully in studies of solar-terrestrial relations. We consider a linear dependence between the radial increment in conifers in Eastern Siberia and solar activity parameters: the length and amplitude of an 11-year solar cycle in the 20th century. It is shown that the increment in conifers in the region is larger in a longer and lower solar cycle than in a short and high one. A correlation between the increment in the width of annual rings of Pinus sylvestris and Siberian pine and the length of the ascending phase of an 11-year cycle is revealed: the longer the ascending phase, the larger the radial increment in conifers. The dynamics of the annual increment in conifers in the region is inversely related to the cycle amplitude and magnetic disturbances in the main solar cycle.     

Transition of solar cycle length in association with the occurrence of grand solar minima indicated by radiocarbon content in tree-rings

In this paper, we review the variation of the 11-year solar cycle since the 15th century revealed by the measurement of radiocarbon content in single-year tree-rings of Japanese cedar trees. Measurements of radiocarbon content in absolutely dated tree-rings provide a calibration curve for accurate dating of archaeological matters, but at the same time, enable us to examine the variations of solar magnetic activity in the pre-historical period. The Sun holds several long-term quasi-cyclic variations in addition to the fundamental 11-year sunspot activity cycle and the 22-year polarity reversal cycle, and it is speculated that the property of the 11-year and the 22-year solar cycle varies in association with such long-term quasi-cycles. It is essential to reveal the details of solar variations around the transition time of solar dynamo for illuminating the mechanisms of the long-term solar variations. We therefore have investigated the property of the 11-year and 22-year cycles around the two grand solar minima; the Maunder Minimum (1645–1715 AD) and the Spoerer Minimum (1415–1534 AD), the periods of prolonged sunspot minima. As a result, slight stretching of the “11-year” and the “22-year” solar cycles was found during these two grand solar activity minima; continuously during the Maunder Minimum and only intermittently during the Spoerer Minimum. On the contrary, normal or slightly shortened 11-year cycles were detected during the interval period of these two minima. It suggests the inverse correlation between the solar cycle length and solar magnetic activity level, and also the change of meridional flow during the grand solar activity minima. Further measurements for the beginning of the grand solar minima will provide a clue to the occurrence of such prolonged sunspot disappearance. We also discuss the effect of solar variations to radiocarbon dating.     

Variations in the large-scale polar solar magnetic flux: The average annual series of the Π index in 1858–2006

A long series of the known Π index of the solar corona structure has been proposed. It seems that this index, which characterizes the limb extension of polar coronal plume systems, is of importance because it is related to the large-scale polar solar magnetic flux. Solar corona photographs and drawings during total solar eclipses, collected for 13 solar activity cycles from different sources (78 eclipses), as well as H-alpha map data on the drift of the high-latitude belt of filaments before polarity reversal of the polar magnetic field have been used. Daily solar corona images, obtained on the SOHO spacecraft (using an EIT ultraviolet telescope), have been additionally used.     

Manifestations of cyclic variations in the solar magnetic field in long-term modulation of cosmic rays

The possibilities of improving the semiempirical model of cosmic ray (CR) modulation, proposed by us previously, are discussed. The following characteristics have been considered as model parameters in order to describe long-period CR variations using a unified model and to more completely reflect solar cycles in CR modulation as a complex interaction between two systems of fields (large-scale and local): the value and sign of the polar solar field, the average strength of the solar magnetic field (the B _ss integral index), partial indices (zone-even (ZE) and zone-odd (ZO) and sector-even (SE) and sector-odd (SO) indices), the tilt of the heliospheric current sheet, and the special index (F _x ) taking into account X ray flares. The role of each index in CR modulation has been revealed. When we described the long-term CR variations using many parameters and taking into account the integral index or one of four partial indices, the best results of modulation modeling during 1976–1999 were obtained for the B _ss total energetic index and SO index. A difference between the model calculations and observations increases beginning from the middle of 2000; the problem features of the CR behavior and the specific features of modeling this behavior in cycle 23 of solar activity (SA) are discussed. It is assumed that a decrease in the CR density at the last SA minimums (from cycle to cycle) can be related to a decrease in the ZO index and to a recently detected similar decrease in the vertical component of the solar dipole magnetic moment.     

Changed relation between sunspot numbers,solar UV/EUV radiation and TSI during the declining phase of solar cycle 23

We study the mutual relation of sunspot numbers and several proxies of solar UV/EUV radiation, such as the F10.7 radio flux, the HeI 1083 nm equivalent width and the solar MgII core-to-wing ratio. It has been noted earlier that the relation between these solar activity parameters changed in 2001/2002, during a large enhancement of solar activity in the early declining phase of solar cycle 23. This enhancement (the secondary peak after the Gnevyshev gap) forms the maximum of solar UV/EUV parameters during solar cycle 23. We note that the changed mutual relation between sunspot numbers and UV/EUV proxies continues systematically during the whole declining phase of solar cycle 23, with the UV/EUV proxies attaining relatively larger values for the same sunspot number than during the several decennia prior to this time. We have also verified this evolution using the indirect solar UV/EUV proxy given by a globally averaged f₀(F2) frequency of the ionospheric F2 layer. We also note of a simultaneous, systematic change in the relation between the sunspot numbers and the total solar irradiance, which follow an exceptionally steep relation leading to a new minimum. Our results suggest that the reduction of sunspot magnetic fields (probably photospheric fields in general), started quite abruptly in 2001/2002. While these changes do not similarly affect the chromospheric UV/EUV emissions, the TSI suffers an even more dramatic reduction, which cannot be understood in terms of the photospheric field reduction only. However, the changes in TSI are seen to be simultaneous to those in sunspots, so most likely being due to the same ultimate cause.     

Solar activity secular cycles

Long-term variations in solar activity secular cycles have been studied using a method for the expansion of reconstructed sunspot number series Sn(t) for 11400 years in terms of natural orthogonal functions. It has been established that three expansion components describe more than 98% of all Sn(t) variations. In this case, the contribution of the first expansion component is about 92%. The averaged form of the 88year secular cycle has been determined based on the form of the first expansion coordinate function. The quasi-periodicities modulating the secular cycle have been revealed based on the time function conjugate to the first function. The quasi-periodicities modulating the secular cycle coincide with those observed in the Sn(t) series spectrum. A change in the secular cycle form and the time variations in this form are described by the second and third expansion components, the contributions of which are about 4 and 2%, respectively. The variations in the steepness of the secular cycle branches are more pronounced in the 200-year cycle, and the secular cycle amplitude varies more evidently in the 2300-year cycle.     

Outer radiation belt of relativistic electrons during the minimum of the 23rd solar cycle

The data on fluxes of electrons with energy Ee > 1 MeV and on radiation doses under the Al shielding of about 2 g/cm² measured on the GLONASS satellite (circular orbit with altitude 20000 km and inclination 65°) for the period from December 2006 through May 2010 are analyzed. The minimum of the 23rd solar cycle turned out to be the longest for all over the space exploration age. Consequently, average semiannual electron fluxes and daily radiation doses are showing the decrease by more than an order of magnitude in comparison with the levels observed in 2007. We present an example of a diffusion wave of relativistic electrons; the wave develops in a period between magnetic storms. This process may result in a significant increase of the radiation dose measured in the orbit, even under the conditions of weak geomagnetic disturbances. The dynamics of variations in relativistic electron fluxes during the magnetic storm of April 5?C6, 2010, is discussed so far as this is the first strong flux enhancement in the 24th solar cycle.     

The QBO effect on the solar signal in the global stratosphere in the winter of the Northern Hemisphere

This paper contains correlations between the NCEP/NCAR global stratospheric data below 10 hPa and the 11-year solar cycle. In the north summer the correlations between the stratospheric geopotential heights and the 11-year solar cycle are strong and positive on the Northern Hemisphere and as far south as 30°S, whereas they are weak in the north winter all over the globe. If the global stratospheric heights and temperatures in the north winter are stratified according to the phase of the QBO in the lower stratosphere, their correlations with the solar cycle are large and positive in the Arctic in the west years of the QBO but insignificantly small over the rest of the earth, as far as the South Pole. In the east years, however, the arctic correlations with the solar cycle are negative, but to the south they are positive and strong in the tropical and temperate regions of both hemispheres, similar to the correlations with the full series of stratospheric data in the other seasons. The influence of the solar cycle in the Arctic is stronger in the latter half of the winter. The global difference, in the northern winter, in the sign and strength of the correlations between the stratospheric heights and temperatures and the solar cycle in east and west years of the QBO can be ascribed to the fact that the dominant stratospheric teleconnection and the solar influence work in the same direction in the east years, but oppose each other in the west years.     

Relation of the F2 region to the parameters of the stratosphere: Comparison of two solar cycles

The results concerning the relation of the stratosphere and ionosphere, obtained on the basis of the data of the 1979–1989 solar cycle, are compared to the data of the following solar cycle. It is shown that all the regularities of the behavior of the correlation coefficient r(h, fo) between the stratospheric parameter h(100) and the critical frequency fo F2 found for the 1980s are also true for the 1990s. Moreover, it turns out that the r(h, fo) dependence on solar activity is similar within both solar cycles.     

Properties of solar activity and ionosphere for solar cycle 25

Based on the known forecast of solar cycle 25 amplitude (Rz _max ≈ 50), the first assessments of the shape and amplitude of this cycle in the index of solar activity F10.7 (the magnitude of solar radio flux at the 10.7 cm wavelength) are given. It has been found that (F10.7)_max ≈ 115, which means that it is the lowest solar cycle ever encountered in the history of regular ionospheric measurements. For this reason, many ionospheric parameters for cycle 25, including the F2-layer peak height and critical frequency (hmF2 and foF2), will be extremely low. For example, at middle latitudes, typical foF2 values will not exceed 8–10 MHz, which makes ionospheric heating ineffective in the area of upper hybrid resonance at frequencies higher than 10 MHz. The density of the atmosphere will also be extremely low, which significantly extends the lifetime of low-orbit satellites. The probability of F-spread will be increased, especially during night hours.     

Long-term modulation of galactic cosmic rays at solar activity minimums

Based on observations of long-term variations in galactic cosmic rays (CRs) on Earth and in the near-Earth space, we have determined, using our own semiempirical model, modulation of galactic CRs during solar cycles 19–23. The modulation model relates CR variations to the characteristics of the solar magnetic field obtained for the surface of the solar wind source at distances of 2.50 and 3.25 solar radii. The main focus is CR behavior at the minimums of cycles 19–23 and specific features of CR modulation at a prolonged (as compared to previous cycles) minimum of cycle 23, which is still ongoing. CR modulation at minimums related to a change in the solar field dipole component during this period of the cycle has been considered. It is indicated that the long-term variations in CRs are better described if the last two years (2007 and 2008) of cycle 23 with anomalously low solar activity (SA) are included in the model. The role and value of the contribution of the cyclic variations in each index used in the proposed CR modulation model to the observed CR modulation have been estimated.     

The effect of solar activity on the secular variation of the geomagnetic field in Romania

The 11-year solar cycle effect in the geomagnetic components H and Z is made clear for Surlari Observatory and 19 repeat stations for the interval 1952–1974. The correlation with Wolf number and its time derivative is discussed in terms of the effects of the external and induced current systems.The $\text{H}\text{?}$ data available for solar cycle 20 (1964–1976) were processed to give the geographical distribution of the secular variation impulse for epoch 1969.5 in Romania. It is suggested that this distribution might reflect the deep internal structure of the area considered.A qualitative correlation is noted between long-period solar activity and variation of the horizontal component of the geomagnetic field at some repeat stations.     

Selected solar wind parameters at 1 AU through two solar activity cycles

In situ measurements of the solar wind largely cover more than two solar magnetic activity cycles, namely 20 and 21. This is a very appealing opportunity to study the influence of the activity cycle on the behaviour of the solar wind parameters. As a matter of fact, many authors so far have studied this topic comparing the long-term magnetic field and plasma averages. However, when the average values are evaluated on a data sample whose duration is comparable with (or even longer than) the solar rotation period we lose information about the contribution due to the fast and the slow solar wind components. Thus, discriminating in velocity plays a key role in understanding solar cycle effects on the solar wind. Based on these considerations, we performed a separate analysis for fast and slow wind, respectively. In particular, we found that: (a) fast wind carries a slightly larger momentum flux density at 1 AU, probably due to dynamic stream-stream interaction; (b) proton number density in slow wind is more cycle dependent than in fast wind and decreases remarkably across solar maximum; (c) fast wind generally carries a magnetic field intensity stronger than that carried by the slow wind; (d) we found no evidence for a positive correlation between velocity and field intensity as predicted by some theories of solar wind acceleration; (e) our results would support an approximately constant divergence of field lines associated with corotating high-velocity streams.     

Great geomagnetic storms in 1841–1870 according to the data from the network of Russian geomagnetic observatories

Great magnetic storms (geomagnetic index C9 is ≥8 for St. Petersburg, which can correspond to Kp ≥ 8 or Dst < ?200 nT), registered from 1841 to 1870 at the St. Petersburg, Yekaterinburg, Barnaul, Nerchinsk, Sitka, and Beijing (at the Russian embassy) observatories are analyzed. A catalog of intensive magnetic storms during this period, which includes solar cycles 9–11, has been compiled. The statistical characteristics of great magnetic storms during this historical period have been obtained. These results indicate that high solar activity played a decisive role in the generation of very intense magnetic storms during the considered period. These storms are characterized by only one peak in a solar cycle, which was registered in the years of the cycle minimum (or slightly earlier): the number of great geomagnetic storms near the solar activity maximum was twice as large as the number of such storms during less active periods. A maximum in September–October and an additional maximum in February are observed in the annual distribution of storms. In addition, the storm intensity inversely depends on the storm duration.     

Forecasting the parameters of sunspot cycle 24 and beyond

Solar variability is controlled by the internal dynamo which is a non-linear system. We develop a physical–statistical method for forecasting solar activity that takes into account the non-linear character of the solar dynamo. The method is based on the generally accepted mechanisms of the dynamo and on recently found systematic properties of the long-term solar variability. The amplitude modulation of the Schwabe cycle in dynamo's magnetic field components can be decomposed in an invariant transition level and three types of oscillations around it. The regularities that we observe in the behaviour of these oscillations during the last millennium enable us to forecast solar activity. We find that the system is presently undergoing a transition from the recent Grand Maximum to another regime. This transition started in 2000 and it is expected to end around the maximum of cycle 24, foreseen for 2014, with a maximum sunspot number R_max=68±17. At that time a period of lower solar activity will start. That period will be one of regular oscillations, as occurred between 1730 and 1923. The first of these oscillations may even turn out to be as strongly negative as around 1810, in which case a short Grand Minimum similar to the Dalton one might develop. This moderate-to-low-activity episode is expected to last for at least one Gleissberg cycle (60–100 years).     

Characteristics of the secular variation of the geomagnetic field between 1964–1981 in Romania

The variation of the H, Z, and T components of the geomagnetic field at repeat stations on Romanian territory between 1964 and 1981 is discussed in terms of internal secular and solar cycle related variations. Their geographical distribution is accounted for by the magnetic and electric structure of the interior of the Earth. The effects of magnetic and electromagnetic induction caused by the solar cycle related variation were evaluated.     

Seasonal and solar cycle variations of the auroral electrojet indices

Using hourly mean auroral electrojet indices for the past 20 years, we examine the seasonal and solar cycle variations of the AU and AL indices as well as the smaller time-scale fluctuations in these indices. The AU and AL indices maximize during summer and equinoctial months, respectively. By removing the effects of the solar conductance from the AU index, it is found that the electric field contribution to the AU index exhibits the same semiannual variation pattern as the AL index, indicating that the semiannual magnetic variations are controlled by the electric field. Since the auroral electrojets are mostly Hall currents flowing in the east–west direction, the fluctuations of the auroral electrojet indices can be interpreted in terms of fluctuations in the north–south component of the electric field and the Hall conductance. The AU fluctuation is largely due to that of the electric field, while the AL fluctuation is attributed to both the electric field and Hall conductance with their contributions being comparable. The high fluctuation of AL compared to that of AU is attributed to particle precipitation associated with substorm activity. However, the fluctuations of the electric field and conductance do not show any noticeable seasonal dependence. The variation pattern of the yearly mean AL index follows the mirror image of the AU index during the past 20 years, indicating that the absolute values of the two indices are proportional to each other. This suggests again that the electric field is the main modulator of magnetic disturbance. On the other hand, they show a tendency to become higher during the declining phase of the solar cycle. This is the same variation pattern confirmed from the aa index. However, the fluctuations of the electric field and the Hall conductance do not show any apparent dependence on the solar cycle.     

Obtaining of information about the IMF evolution from an analysis of the geomagnetic field data

A comparison of the time variations in the geomagnetic field characteristics (the u and aa indices of geomagnetic activity) with the variation in the solar magnetic dipole inclination shows close agreement between these variations. The linear correlation coefficients between the u and aa indices, the u index and solar magnetic dipole inclination, and the aa index and solar magnetic dipole inclination are 0.93, 0.45, and 0.49, respectively. This makes it possible to extend studying the IMF evolution in the 11-year cycle of solar activity to the 170-year period beginning from 1835. It has been indicated that the time variation in the heliospheric current sheet (HCS) surface deviation from the solar magnetic equator plane, calculated based on the actual HCS configuration, is in good agreement with the time variation in the amplitude of the Fourier series second harmonics in a harmonic analysis of the series of daily data on the IMF sign in the vicinity of the Earth. The linear correlation coefficient is 0.9 in this case.